{
  "id": "0902.3482",
  "version": "v2",
  "published": "2009-02-19T23:02:33.000Z",
  "updated": "2010-01-10T11:58:33.000Z",
  "title": "Some Additive Combinatorics Problems in Matrix Rings",
  "authors": [
    "Ron Ferguson",
    "Corneliu Hoffman",
    "Florian Luca",
    "Alina Ostafe",
    "Igor Shparlinski"
  ],
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-01-10T11:58:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11C20",
      "11D79",
      "11T06"
    ],
    "keywords": [
      "matrix rings",
      "additive combinatorics problems",
      "largest prime divisor",
      "finite fields",
      "unimodular matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.3482F"
    }
  }
}